Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

The difference of cubes of two consecutive natural numbers is 1657. Find the numbers.

Sagot :

naǫ
x, x+1 - two consecutive natural numbers

[tex](x+1)^3-x^3=1657 \\ x^3+3x^2+3x+1-x^3=1657 \\ 3x^2+3x+1=1657 \\ 3x^2+3x-1656=0 \\ 3x^2+72x-69x-1656=0 \\ 3x(x+24)-69(x+24)=0 \\ (3x-69)(x+24)=0 \\ 3x-69=0 \ \lor \ x+24=0 \\ 3x=69 \ \lor \ x=-24 \\ x=23 \ \lor \ x=-24[/tex]

x must be a natural number, so x=23.

[tex]x=23 \\ x+1=23+1=24[/tex]

The numbers are 23 and 24.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.